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Quasilinear elliptic equations on noncompact Riemannian manifolds
University of Mediterranea Reggio Calabria, Italy.
University of Florence, Italy.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. RUDN University, Russia.
2017 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 273, no 11, 3426-3462 p.Article in journal (Refereed) Published
Abstract [en]

The existence of solutions to a class of quasilinear elliptic problems on noncompact Riemannian manifolds, with finite volume, is investigated. Boundary value problems, with homogeneous Neumann conditions, in possibly irregular Euclidean domains are included as a special instance. A nontrivial solution is shown to exist under an unconventional growth condition on the right-hand side, which depends on the geometry of the underlying manifold. The identification of the critical growth is a crucial step in our analysis, and entails the use of the isocapacitary function of the manifold. A condition involving its isoperimetric function is also provided. (C) 2017 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2017. Vol. 273, no 11, 3426-3462 p.
Keyword [en]
Quasilinear elliptic equations; Sobolev embeddings; Noncompact manifolds; Neumann problems
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-142417DOI: 10.1016/j.jfa.2017.08.018ISI: 000412969900003OAI: oai:DiVA.org:liu-142417DiVA: diva2:1153701
Note

Funding Agencies|MIUR (Italian Ministry of Education, University and Research) [2012TC7588]; GNAMPA of the Italian INdAM (National Institute of High Mathematics); Ministry of Education and Science of the Russian Federation [02.a03.21.0008]

Available from: 2017-10-31 Created: 2017-10-31 Last updated: 2017-11-06

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Mazya, Vladimir
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